Even though this analysis has been performed only up to first order in the coupling constant, one can already draw parallels with existing BMS results for the full Einstein theory at null and spatial infinity. The BMS analysis at spatial infinity involves some subtleties that can be better understood in the linearized theory of gravity, for instance, the canonical realization of boost generators [1]}. In the same spirit, our perturbative approach in the light-cone formalism offers an unconventional insight into the structure of the BMS symmetry. Another similarity with the spatial infinity analysis is that the invariance of the Hamiltonian reduces the parameters, \(Y\)  and \(\overline{Y}\) , to Lorentz rotations, thereby eliminating superrotations [2]} from the theory. There are several ways to interpret the BMS symmetry in gravity apart from the original work of [3]}, [4]}, [5]} as the enhancement of the Poincaré algebra with angle-dependent supertranslations. In [6]}, for instance, the BMS algebra was argued to be the conformal extension of the Carroll algebra on null hypersurfaces. In light-cone gravity, we present a new interpretation of the BMS symmetry as the local extension of the dynamical part of the Poincaré algebra in Dirac's front form analysis [7]}. Light-cone gravity offers a straightforward approach to study the BMS symmetry in a physical gauge, which might help us better understand its connection with on-shell amplitudes and soft theorems [8]}, [9]}.
